How to Make It
Combine strawberries, simple syrup, verjus, and salt in a blender. Process until smooth, about 1 minute. Pour through a fine wire-mesh strainer into a 13- x 9-inch freezer-safe baking dish or rimmed baking sheet. Transfer to freezer, and freeze 4 hours, scraping with a fork every 40 minutes to create small ice crystals.
While granita freezes, place basil, mint, grapeseed oil, pine nuts, olive oil, and honey in a food processor. Scrape seeds from vanilla bean pod into food processor; discard pod. Process until smooth, about 2 minutes.
To serve, spoon granita into bowls, and top with whipped cream and sweet pesto.